The notes of the Harmonic series are fine for bugle calls and trumpet calls:

However playing melody requires access to all the notes in between. For this we need to find ways of playing the additional notes to fill in the gap between the Harmonics. Brass instruments create lower pitches by adding additional lengths of tubing.

If we consider the gap from Harmonic 2 to Harmonic 3 we notice that we need 7 half steps to play all the notes between these. (Harmonic 1 is not usable on the trumpet although it is usable on the larger brass instruments.)

The basic design of the modern brass instrument adds three different loops of tubing: half step, whole step, and one and a half steps. The loops are switched in and out by valves. 

These valves, which are operated by the player’s fingers, are employed singly, or together, to give all the musical intervals from a minor second to an augmented fourth (seven half steps lower); a full chromatic scale between Harmonic 2 and Harmonic 3.

Lower brass instruments are often fitted with four or more valves to gain access to the full octave between Harmonic 1 and Harmonic 2. 

The trombone has a telescoping slide with infinitely variable additional lengths from zero to augmented fourth.